Vehicle wheel balancer system

ABSTRACT

A method for providing a centering check for a rotating body mounted on a wheel balancer based on measuring at least one imbalance parameter and for determining weight display thresholds for static and dynamic imbalance correction weights which vary with parameters of the wheel and/or tire. The rotating body is mounted on a spindle of the wheel balancer and an imbalance parameter or runout measurement taken. The mounting of the rotating body on the spindle is then altered, and a second measurement of the imbalance parameter or runout is taken. A processor in the wheel balancer determines if the difference between the first and second measurements exceeds a predetermined threshold value, indicative of off-center mounting of the rotating body one the spindle. Upon centered mounting of the rotating body, imbalance measurements are acquired, and required correction weights are displayed to an operator if they exceed an identified imbalance threshold level.

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] The present application is a continuation in part of, and claimspriority from, co-pending U.S. patent application Ser. No. 10/455,623filed on Jun. 5, 2003.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH

[0002] Not Applicable.

BACKGROUND OF THE INVENTION

[0003] The present invention relates generally to automotive serviceequipment designed to measure imbalance in a vehicle wheel assembly, andin particular, to an improved wheel balancer system configured to adjustan imbalance correction threshold level and to check centering of wheelsmounted to the wheel balancer system.

[0004] Wheel balancer systems are designed to determine characteristicsof a rotating body such as a wheel assembly consisting of a wheel rimand a pneumatic tire, or of a wheel rim alone. The determinedcharacteristics include, but are not limited to static imbalances,dynamic imbalances, lateral forces, radial forces and runout parameters.Determination of some of these characteristics result from directmeasurements, while others are obtained from an analysis of themechanical vibrations caused by rotational movement of the rotatingbody. The mechanical vibrations are measured as motions, forces, orpressures by means of transducers mounted in the wheel balancer system,which are configured to convert the mechanical vibrations intoelectrical signals.

[0005] Existing wheel balancer systems suffer from subtle deficienciesin connection with providing compensation for run-out and in tire to rimmatching procedures. These systems, such as the GSP9700 Seriesmanufactured by Hunter Engineering Co. of Bridgeton, Mo. are capable ofdisplaying an angular location at which a pneumatic tire should bemounted to a wheel rim to minimize an overall radial force variationassociated with the wheel assembly. For an accurate measurement of rimrunout at the beadseat of the tire, it is necessary for the rim runoutto be measured without the tire mounted thereon, and then for the rim tobe dismounted from the balancer, and the tire mounted to the rim. Thewheel assembly consisting of the tire and rim is then remounted to thebalancer to measure the force variations associated therewith. Anycentering difference with respect to the initial and subsequent mountingof the rim and wheel assembly on the balancer spindle will result inerrors in the determination of the rim runout, the assembly forcevariation, and the tire force variation computations. This “centeringerror” can become even more significant with larger wheel assembles,such as those currently entering the market.

[0006] There are many types of adaptors for use when mounting andcentering wheels onto a balancer spindle. Common examples of adaptorsare cones, centering sleeves, flange plates with rigid pins, flangeplates with compliant pins, clamp cups and other devices as can be seenin publications such as Hunter Engineering Company accessory brochure,Form No. 3203T, entitled “Wheel Balancer Accessories”. Often there areseveral different adaptors that may be used to mount a wheel on a wheelbalancer. Due to variations in wheel design there are usually severaladaptors, or combinations of adaptors, that appear to fit the wheel, butactually do not center the wheel adequately on the wheel balancer shaft.Accordingly, it is desired to develop a solution to aid the operator inselecting the best adaptor for a wheel.

[0007] One solution to the centering error problem induced by thedismounting and remount of a wheel rim or wheel assembly on a balancersystem spindle is addressed in U.S. Pat. No. 6,481,282 B2 for “WheelBalancer System With Centering Check”. The solution set forth in the'282 patent requires that the wheel rim runout be measured before andafter the wheel rim is dismounted from the balancer system, and acomparison carried out. If the comparison of the two runout measurementsindicates a difference which is greater than a predetermined threshold,it is assumed that the wheel rim has not been properly centered on thebalancer spindle during the remounting procedure, and a warning isprovided to the operator. The solution presented in the '282 patentfurther requires that the wheel balancer system include the capacity tomeasure and store wheel rim runout parameters (i.e. magnitude and phase)for subsequent comparisons with predetermined threshold values.

[0008] As not all wheel balancer systems are capable of measuring wheelrim runout, it would be a particular advantage for a wheel balancersystem to incorporate a centering check process which does not require ameasurement of wheel rim runout both before and after altering thebalancer mounting of the of a wheel rim or wheel assembly.

[0009] While accurate centering of a wheel rim or wheel assembly on abalancer is important to obtain accurate measurements of any imbalancepresent therein, it is additionally important to provide an operatorwith information about whether or not there is a need to correct adetected imbalance in the wheel rim or wheel assembly, or if thedetected imbalance is sufficiently small so as to have a negligibleeffect on vehicle performance and handling. Currently, wheel rim sizesin the U.S. market range from 13.0 inches in diameter up to andincluding the present DOT limit of 24.0 inches in diameter. It isanticipated that wheel rim sizes will increase to 26.0 inches indiameter in the near future, with a corresponding increase in associatedtire sizes. A problem presented by the continued increase in wheel rimand wheel assembly sizes is the effect of a fixed imbalance correctionthreshold level.

[0010] Due to the limited size increments in which imbalance correctionweights are available, conventional balancer systems are configured todisplay as zero any required imbalance correction weight values below apredetermined threshold. Typically the predetermined threshold is 0.29oz., and is selected to be slightly greater than the smallest imbalancecorrection weight increment, regardless of the size of the wheel rim orwheel assembly. This can result in an operator “chasing” weights on asmall or narrow wheel due to the significant effect of the thresholdlevel on imbalances, and a poor balance on larger diameter wheels due toa reduced effectiveness of the threshold level. One solution is shown inU.S. Pat. No. 6,484,574 to Douglas, in which a balancer is configured toselect the best weight plane locations from data acquired by scanningthe rim profile. This is an advantageous method, but it is noteconomical for all balancers to have this feature.

[0011] Clearly, it would be further advantageous to provide a wheelbalancer system with a method for determining an imbalance correctionthreshold level which varies in relation to the dimensions of the wheelassembly undergoing balancing in addition to the incremental size of theimbalance correction weight employed, and which provides an operatorwith a scaled visual indication of any remaining imbalances presentafter application of suggested imbalance correction weights at suggestedweight placement locations.

BRIEF SUMMARY OF THE INVENTION

[0012] Briefly stated, in a first aspect of the present invention amethod of balancing a rotating body includes the steps of mounting thebody on a spindle of a balancer, measuring at least one imbalanceparameter of the body, altering the mounting of the body on the spindleof the balancer, obtaining a second measurement of the at least oneimbalance parameter of the body, calculating a difference between saidfirst measurement and said second measurement for said at least oneimbalance parameter, and comparing the calculated difference with apredetermined threshold amount to determine whether the rotating body isproperly centered on the balancer spindle.

[0013] In a second aspect of the present invention, a method ofbalancing a rotating body includes the steps of determining an imbalancecorrection weight placement diameter and an imbalance correction weightplacement separation distance, utilizing the determined placementdiameter together with a predetermined imbalance force limit to identifya static imbalance threshold, and utilizing the determined separationdistance and weight placement diameter together with a predeterminedimbalance moment limit to identify a dynamic imbalance threshold.

[0014] In a third aspect of the present invention, a method of balancinga rotating body includes the steps of determining one or more imbalancecharacteristics of the rotating body, identifying one or more imbalancecorrection weight amounts and placement locations, and providing ascaled visual display of any imbalance present in the rotating bodyprior to, or following, application of the one or more imbalancecorrection weight amounts at the identified placement locations

[0015] The foregoing and other objects, features, and advantages of theinvention as well as presently preferred embodiments thereof will becomemore apparent from the reading of the following description inconnection with the accompanying drawings.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

[0016] In the accompanying drawings which form part of thespecification:

[0017]FIG. 1 is a diagrammatic view illustrating a generic wheelbalancer suitable for use with the present invention;

[0018]FIG. 2 is a simplified top plan view illustrating an alternategeneric wheel balancer suitable for use with the present invention;

[0019]FIG. 3 is a block diagram illustrating various parts of a genericwheel balancer of FIG. 1 or FIG. 2;

[0020]FIG. 4 is a flow chart diagram of a method of the presentinvention for centering a rotating body on a balancer spindle;

[0021]FIG. 5 is a representation of a prior art balancer displayindicating no required weight placement for a rotating body of specificdimensions;

[0022]FIG. 6 is a representation of a prior art balancer display similarto FIG. 5, indicating a required weight placement for the rotating bodywith smaller diameter dimensions but having the same imbalance;

[0023]FIG. 7 is a representation of a prior art balancer displayindicating required weight placement for a rotating body of specificdimensions;

[0024]FIG. 8 is a representation of a prior art balancer display similarto FIG. 7, indicating no required weight placements for the rotatingbody with larger width (weight plane separation) dimensions but havingthe same imbalance;

[0025]FIG. 9 is a flow chart diagram of a method of the presentinvention for displaying desired correction weights;

[0026]FIG. 10A is a two dimensional graphical representation of theblind amount versus wheel diameter for a predetermined static imbalancelimit;

[0027]FIG. 10B is a surface plot representation of the blind amountcompared with wheel diameter and tire diameter for a predeterminedstatic imbalance limit;

[0028]FIG. 11A is a surface plot representation of wheel rim diameter,wheel width, and couple blind amount for a predetermined coupleimbalance limit;

[0029]FIG. 11B is a surface plot similar to FIG. 11A, for tire diameter,wheel width, and couple blind amount for a predetermined coupleimbalance limit;

[0030]FIG. 12 is a representation of a display of the present inventionshowing a graphical presentation of the imbalance forces in the rotatingbody;

[0031]FIG. 13 is a representation of a display similar to FIG. 12,indicating that no additional weight is required on the wheel with asmaller diameter dimension and having the same imbalance;

[0032]FIG. 14 is a representation of a display of the present inventionshowing a graphical presentation of the imbalance forces in the rotatingbody; and

[0033]FIG. 15 is a representation of a display similar to FIG. 12,indicating that less weight is required on a wheel with larger width(weight plane separation) dimensions but having the same imbalance.

[0034] Corresponding reference numerals indicate corresponding partsthroughout the several figures of the drawings.

DESCRIPTION OF THE PREFERRED EMBODIMENT

[0035] The following detailed description illustrates the invention byway of example and not by way of limitation. The description clearlyenables one skilled in the art to make and use the invention, describesseveral embodiments, adaptations, variations, alternatives, and uses ofthe invention, including what is presently believed to be the best modeof carrying out the invention.

[0036] Turning to the drawings, FIG. 1 illustrates, in simplified form,the mechanical aspects of a wheel balancer 10 suitable for the presentinvention. The particular balancer shown is illustrative only, since theparticular devices and structures used to obtain dimensional andimbalance information related to a rotating body could be readilychanged without changing the present invention.

[0037] Balancer 10 includes a rotatable shaft or spindle 12 driven by asuitable drive mechanism such as a motor 14 and drive belt 16. Mountedon spindle 12 is a conventional optical shaft encoder 18 which providesspeed and rotational position information to the central processing unit20, shown in FIG. 3.

[0038] During the operation of wheel balancing, at the end of thespindle 12, a rotating body 22 under test is removably mounted forrotation with the spindle hub 12A. The rotating body 22 may comprise awheel rim, or a wheel assembly consisting of a wheel rim and a tiremounted thereon. To determine the rotating body imbalance, the balancerincludes at least a pair of imbalance force sensors 24 and 26, such aspiezoelectric sensors or strain gauges, coupled to the spindle 12 andmounted on the balancer base 28.

[0039] Turning to FIG. 2, it can be seen that the actual construction ofthe mechanical aspects of the balancer 10 can take a variety of forms.For example, the spindle 12 can include a hub 12A against which therotating body 22 abuts during the balancing procedure.

[0040] When a rotating body 22 is unbalanced, it vibrates in a periodicmanner as it is rotated, and these vibrations are transmitted to thespindle 12. The imbalance sensors 22 and 24 are responsive to thesevibrations in the spindle 12, and generate a pair of analog electricalsignals corresponding to the phase and magnitude of the vibrations atthe particular sensor locations. These analog signals are input to thecircuitry of FIG. 3, described below, which determines the requiredmagnitudes and positions of correction weights necessary to correct theimbalance.

[0041] Turning to FIG. 3, wheel balancer 10 includes not only theimbalance sensors 22 and 24, and spindle encoder 18, but also thecentral processing unit 20 (such as a microprocessor, digital signalprocessor, or graphics signal processor). The central processing unit 23performs signal processing on the output signals from the imbalancesensors 22 and 24 to determine an imbalance in the rotating body. Inaddition, the central processing unit 20 is connected to and controls adisplay 30 which provides information to an operator, control motor 14through associated motor control circuits 32, and keeps track of thespindle rotation position with encoder 18.

[0042] Balancer 11 further includes one or more manual inputs 34, suchas a keyboard, control knobs, or selector switches, which are connectedto the central processing unit 20. The central processing unit 20 hassufficient capacity to control, via software, all the operations of thebalancer 10 in addition to controlling the display 30. The centralprocessing unit 20 is connected to a memory such as an EEPROM memory 36,EPROM program memory 38, and a dynamic RAM (DRAM) memory 40. The EEPROMmemory 36 is used to store non-volatile information, such as calibrationdata, while the central processing unit 20 uses the DRAM 40 for storingtemporary data.

[0043] The central processing unit 20 is also connected to ananalog-to-digital converter 42. The signals from the imbalance sensors22 and 24 are supplied through anti-aliasing circuitry 44A and 44B (ifneeded) to the analog-to-digital converter 42.

[0044] The operation of the various components described above is fullyset forth in U.S. Pat. No. 5,396,436, the disclosure of which isincorporated herein by reference. It should be understood that the abovedescription is included for completeness only, and that various othercircuits could be used instead.

[0045] In a first embodiment of the present invention, the balancer 10is configured with software to provide an operator with an option toperform a centering check to ensure that the rotating body 22 isaccurately mounted to the spindle 12. As shown in FIG. 4, after mountingthe rotating body 22 on the balancer spindle (Box 100), and an initialmeasurement of at least one imbalance parameter, such as a raw forcetransducer output, an imbalance magnitude, an imbalance angularlocation, or the mass of the rotating body, is obtained (Box 102), thecentering check is performed by first loosening a wing nut or othermounting device securing the rotating body 22 to the spindle 12. Withthe mounting device loosened, the mounting of the rotating body 22 aboutthe spindle is altered (Box 104), and the wing nut or other mountingdevice retightened. The altering of the mounting may involve eitherremoving the rotating body 22 from the spindle 12 and replacing itthereon, or simply rotating the rotating body 22 about the axis of thespindle 12.

[0046] With the rotating body 22 in the altered mounting position, asecond measurement of the previously measured, at least one imbalanceparameters is conducted (Box 106). The central processing unit 20compares the previous measurements with the second measurements takenafter the altering of the rotating body mount on the spindle 12 toidentify a difference between the two measurements (Box 108). Thecalculated difference is then compared with a predetermined threshold ortolerance (Box 110). If the results of the comparison indicate themeasurements deviate by more than a predetermined amount (Box 112), thecentral processing unit 20 causes a message to be shown on the display30 warning of a detected mis-centering of the rotating body 22 on thespindle 12.

[0047] To correct a mis-centering of the rotating body 22 on the spindle12, the central processing unit 20 provides directions to the operatoron display 30, requesting that the operator repeat the step of alteringthe mounting of the rotating body 22 on the spindle 12. Once therotating body 22 is re-mounted on the spindle 12 in an altered position,the central processing unit obtains an additional measurement of thepreviously measured imbalance parameters. This process is repeated untilthe results of a comparison of the most recently obtained measurementsand any previously obtained measurements do not deviate by more than apredetermined amount, i.e. indicating that the rotating body 22 iscentered to within the predetermined tolerance (Box 114).

[0048] The principle reasoning behind the centering check methodologyset forth above is that an operator is more likely to properly centerthe rotating body 22 on the spindle 12 at least twice, and less likelythat an operator will mis-center the rotating body 22 twice in the sameway, producing nearly identical measurements of the imbalanceparameters. Hence, the central processing unit is configured to considerthe rotating body 22 to be properly centered upon the spindle 12 thefirst time the results of the comparison do not indicate a deviation ofmore than a predetermined amount between the most recent measurement andany previous measurements of the imbalance parameters.

[0049] Optionally, the central processing unit 20 may be configured toterminate the centering check procedure, and provide a suitable warningon display 30 to the operator if a predetermined number of mis-centeredmountings are detected in sequence. If an operator is unable to properlycenter the rotating body 22 on the spindle 12 within a predeterminednumber of tries, it is likely that the centering deviations are not theresult of operator mounting error, but rather, are the result of damageto the rotating body 22, spindle 12, or mounting device, or possibly thewrong adaptor is selected to be used to secure the rotating body 22 tothe spindle 12.

[0050] In an alternate embodiment of the present invention for use whenthe rotating body 22 is a wheel rim and tire assembly, the runout of thetire mounted on the wheel rim is obtained in place of the measurement ofthe imbalance parameter. This runout measurement may be made by a devicethat contacts the outermost diameter of the tire as the tire rotates.For example, an arm with a roller secured thereto, such as is providedwith the Hunter GSP9700, or an arm with a fixed surface disposed on theend. Alternatively, the tire outer diameter can be measured by aconventional non-contact tire measurement device, such as an ultrasonicsensor, a laser, or a capacitive proximity sensor. Also alternatively,the lateral runout of the tire sidewall, or any surface on the side ofthe assembly, can be measured (by a contacting device, or non-contactingdevice) instead of, or in addition to, radial runout.

[0051] After an initial measurement of the tire runout is obtained andstored, the centering check is performed by first loosening a wing nutor other mounting device (not shown) securing the rotating body 22 tothe spindle 12. With the mounting device loosened, the mounting of therotating body 22 about the spindle is altered, and the wing nut or othermounting device (not shown) retightened. The altering of the mountingmay involve either removing the rotating body 22 from the spindle 12 andreplacing it thereon, or simply rotating the rotating body 22 about thean axis of the spindle 12.

[0052] With the rotating body 22 in the altered mounting position, asecond measurement of the previously measured tire runout is conducted.The central processing unit 20 compares the previous measurements withthe second measurements taken after the altering of the rotating bodymount on the spindle 12. If the results of the comparison indicate themeasurements deviate by more than a predetermined amount, where thepredetermined amount may be a constant or a variable based on wheel/tiresize, mass or other parameter, the central processing unit 20 causes amessage to be shown on the display 30 warning of a detectedmis-centering of the rotating body 22 on the spindle 12, so thatsuitable corrective action may be taken by the operator.

[0053] Once a rotating body 22 is accurately centered on the balancerspindle 12, the balancer 10 can begin the process of measuring one ormore imbalance parameters of the rotating body 22, and providing theoperator with one or more suggested imbalance correction weightmagnitudes and placement locations. Imbalance correction weightmagnitudes and placement locations are calculated and displayed to anoperator on a screen or numerical readout 30. Due to the limited sizeincrements in which imbalance correction weights are usually available,conventional balancer systems are configured to display to the operatora zero value for any imbalance which would require the installation ofan imbalance correction weight amount which is below a predeterminedthreshold.

[0054] Typically the predetermined threshold is selected to be slightlygreater than the smallest imbalance correction weight increment,regardless of the size of the wheel rim or wheel assembly. For a systemadapted to use imbalance correction weights having 0.25 oz. increments,an exemplary threshold limit is 0.29 oz. of imbalance. This can resultin an operator “chasing” weights on a small or narrow wheel due to theinsignificant effect of the threshold level on imbalances, and a poorbalance on larger diameter wheels.

[0055] For example, as shown in FIG. 5, a wheel having a 6.0 inch axialwidth, and a 15.0 inch diameter might require imbalance weights belowthe predetermined weight threshold, resulting in the balancer displayingto an operator that no imbalance correction weights are required foreither the left or right imbalance correction planes. However, as shownin FIG. 6, if the dimensions of the wheel are manually changed by theoperator using the “SET DIMENSIONS” button 150 to indicate a 5.0 inchaxial width and a 14.0 inch diameter, without re-measuring the wheelimbalance, larger weights are displayed to correct the imbalance, whichexceed the predetermined weight threshold level. As a result, aconventional balancer would now direct an operator to install weights inthe left and right imbalance correction planes (as indicated by arrows152) despite the fact that the amount of the imbalance is unchanged.

[0056] A similar problem exists for conventional balancer systems whenbalancing large wheels. For example, as shown in FIG. 7, a wheel havingan 8.0 inch axial width, and a 16.0 inch diameter might have animbalance above the predetermined weight threshold, resulting in thebalancer displaying to an operator that imbalance correction weights arerequired for both the left or right imbalance correction planes.However, as shown in FIG. 8, if the dimensions of the wheel are manuallychanged by the operator using button 150 to show an 18.0 inch diameter,without re-measuring the wheel imbalance, less weight is displayed tocorrect the imbalance, which drops below the predetermined weightthreshold level. As a result, a conventional balancer would now indicateto an operator that no weights in the left and right imbalancecorrection planes are required, despite the fact that the amount of theimbalance is unchanged.

[0057] In an alternate embodiment of the present invention, the balancer10 is provided with a predetermined value representative of the maximumimbalance effect which is permitted for each type of imbalance in therotating body 22 to be corrected, i.e., for static imbalance and fordynamic imbalance. For example, a predetermined static imbalance momentlimit is provided to identify a static imbalance threshold, and apredetermined dynamic imbalance moment limit is provided to identify adynamic imbalance threshold. Preferably, the predetermined limits areselected to correspond to a level of imbalance moments in the rotatingbody 22 which are imperceptible to the average consumer, such as 2.18oz.-in. for a static imbalance moment limit, corresponding to a 0.29 oz.weight on a 15″ diameter wheel rim, and 15.0 oz.-in². for a dynamicimbalance limit which corresponds to approximately a 0.33 oz. weight ona 6″ wide, 15″ diameter wheel rim. It may be desirable, however, toadjust these limits to favor either static imbalance or dynamic (couple)imbalance. For instance, it is understood that passengers in a vehicleare less sensitive to a dynamic (couple) imbalance than a staticimbalance. A way to reduce technician's labor with a minimal increase invibration would be to increase the dynamic limit to 20.0 oz.-in².

[0058] In a second alternate embodiment of the present invention, shownin FIG. 9, a balancer 10 is configured to select an imbalance correctionweight display threshold based upon one or more dimensions of therotating body 22 being balanced. These dimensions include the imbalancecorrection weight placement diameter and an imbalance correction weightplacement separation distance. Preferably, these dimensions are measureddirectly by the balancer 10 utilizing operator assistance to place ameasuring device, such as a dataset arm, at the desired imbalancecorrection weight planes and/or at the edge of the rotating body 22.Alternatively, when the diameter and width of a rotating body 22 areknown, an operator can directly supply the balancer 10 withcorresponding values using one or more manual inputs 34 (Box 200).

[0059] The balancer 10 is configured to utilize the predetermined valuerepresentative of the maximum imbalance effect permitted, together withthe associated dimensions of the rotating body 22 to identify a variableimbalance correction threshold used to display, to an operator ondisplay 30, as zero any imbalance which would require an imbalancecorrection weight value below the variable threshold. (Box 204).

[0060] For correcting static imbalances present in the rotating body 22(Box 206), the predetermined static imbalance moment limit is F_(max)(typically in units of oz.-in.), the known or measured rotating bodydiameter is D, and the imbalance correction threshold or “blind” isW_(BS). A variable threshold value for W_(BS) is determined by thebalancer 10 according to the following equation:

W _(BS) =F _(MAX)/(D/2)  Equation (1)

[0061] For correcting dynamic imbalances present in the rotating body 22(Box 208), the predetermined dynamic imbalance moment limit is M_(max),(typically in units of oz.-in.²) the known or measured rotating bodyaxial length or axial width is W, and the imbalance correction thresholdor “blind” is W_(BD). If it is assumed that there is no static imbalancein the wheel, a variable threshold value for W_(BD) is determined by thebalancer 10 according to the following equation:

W _(BD) =M _(max) /W*(D/2)  Equation (2)

[0062] For example, if the balancer 10 is configured with apredetermined static imbalance moment limit (F_(max)) of 2.18 oz.-in.for correcting static imbalances present in the rotating body 22, andthe rotating body 22 has a measured or known diameter of 15.0″, solvingEquation (1) above for W_(BS) yields an imbalance correction thresholdor “blind” of 0.29 oz. If the rotating body 22 has a measured or knowndiameter of 12.0″, Equation (1) yields an imbalance correction thresholdor “blind” of 0.36 oz. Correspondingly, if the rotating body 22 has ameasured or known diameter of 20.0″, Equation (1) yields an imbalancecorrection threshold or “blind” of 0.21 oz. for the same value ofF_(max).

[0063] The benefit offered by a balancer 10 configured to utilize theaforementioned methods to identify imbalance correction thresholds basedin-part upon the known or measured dimensions of a rotating body 22undergoing balancing can be clearly illustrated by the followingcomparisons.

[0064] When balancing a wheel assembly having a 15.0″ diameter wheel rimwith an axial width of 5.0″, it is possible for a conventionallyconfigured balancer to identify a static imbalance over the limit of2.18 oz.-in. but a dynamic couple under the limit of 15 oz.-in.² andsuggest a correction requiring two imbalance correction weights of 0.25oz. and 0.75 oz., one to be placed on the inner lip of the wheel rim,and the other to be placed on the outer lip of the wheel rim. However,on a balancer 10 configured with a predetermined dynamic imbalancemoment limit (M_(max)) of 15.0 oz.in², the dynamic couple is determinedto have minimal effect on the vehicle and will be ignored and theremaining static imbalance can be corrected by a single 0.25 oz. weight.

[0065] By setting the imbalance threshold amounts based on the actualforce and moment values, rather than displayed weight amounts, it ispossible to minimize the residual imbalance in a wheel. A conventionalbalancer may measure a purely static imbalance that requires 0.50 oz.weight to correct. If the balancer is set to the “Dynamic” balance modeit will calculate that a 0.25 oz. weight is required on both the leftand the right planes. Since the traditional threshold is set to 0.29 oz.the machine will show that no correction weights are required, but thewheel is not balanced. With the method of the present inventionemployed, the correct weights will be displayed and the wheel will beproperly balanced. In the example described above, there is a smallamount of couple imbalance present along with the static imbalance. Eventhough the amount of couple is small and no specific weights arerequired to correct it, it is possible to place the static correctionweight in a location to possibly reduce the couple imbalance.

[0066] When correcting the static imbalance, the single static weightcan be placed on either the inner plane, adjacent the balance, or theouter plane, opposite the balancer. The inner plane is alternativelyreferred to as the left plane, when the wheel is mounted on the rightside of a balancer, and the outer plane is alternatively referred to asthe right plane for the same wheel placement. To choose the correctplane in which to place the single static weight, it is necessary tocompare the phase of the dynamic couple vector to the phase of thestatic force vector. The static correction weight is placed on the planethat minimizes the residual dynamic couple imbalance, without theplacement of additional couple imbalance correction weights.

[0067] This will correct the static imbalance (which was greater thanthe blind), and depending upon the difference between the couple andstatic imbalance phase, it will decrease the couple imbalance or leaveit unchanged (couple imbalance was already acceptably low). Since theinner and outer plane couple imbalance phases are always 180 degreesapart, the static imbalance phase will never be more than 90 degreesaway from one of the couple imbalance phases. If the difference betweenthe static and one of the couple imbalance phases is small, there willbe a significant improvement in couple imbalance. If the staticimbalance phase is exactly 90 degrees between both couple imbalancephases, the couple imbalance will not change when the static correctionweight is added. This can be accomplished by the following logicsequence:

[0068] Assume the balancer is in “Dynamic” mode, static imbalance isgreater than blind, and couple imbalance is less than the predeterminedblind. The following steps are taken to place a single weight that willcorrect the static imbalance while reducing (or not changing) the coupleimbalance.

[0069] Let couple imbalance=0 and calculate the static correctionweight.

[0070] Static weight magnitude=Static imbalance/radius

[0071] Static weight phase=Static imbalance phase+180 degrees.

[0072] To correct the static imbalance, this weight could be placed oneither the inner plane or the outer plane.

[0073] If the difference between the static imbalance phase angle andthe outer plane couple imbalance phase angle is less than 90 degrees,place the single static correction weight on the outer plane. Otherwise,place the weight on the inner plane.

[0074] If the balancer is in “Static” mode it is common that dimensionswill only be entered for a single plane. With the present invention itis desirable to compare the absolute dynamic couple imbalance to thedynamic couple threshold. If the absolute dynamic couple exceeds thethreshold it is desirable to provide an indicator to the operator ofthis condition. The indication may be in the form of blinking lights,alpha-numeric text, or in the form of a message. If the operator hasentered dimensions for two planes the indicator may be in the form of adisplay of the weights required to correct the couple imbalance.

[0075] To aid an operator in determining if a rotating body 22 has beenbalanced to within a predetermined threshold for both static imbalanceand dynamic imbalance, the balancer 10 in an alternate embodiment isconfigured to provide the operator with a graphical illustration 300 ofthe measured imbalances relative to the threshold level of absoluteimbalances on display 30, i.e. the couple imbalance threshold and thestatic imbalance threshold. Conventionally, such as shown in U.S. Pat.No. 5,915,274 to Douglas, weights required to correct static and dynamicimbalances are displayed relative to a fixed weight amount threshold toan operator on a bar graph. The fixed weight amount is based on theincremental weight size and the vehicle wheel geometry. In contrast, thegraphical illustration 300 of the present invention displays informationto an operator based upon absolute imbalances, and not on theincremental weight sizes and vehicle wheel geometry.

[0076] Turning to FIGS. 12 and 13, a display 30 from a balancer 10configured with the features of the present invention is shown first fora wheel having an axial length or width of 6.0 inches and a diameter of15.0 inches. In this example, the imbalance present in the wheel forboth static and dynamic imbalance is below a threshold level. This isillustrated with the graphical illustration 300, incorporating a slidingscale 302 for static imbalance, and a sliding scale 304 for dynamicimbalance. On each sliding scale 302 and 304, shown in FIG. 12, thecomputed imbalance amounts, as indicated by the arrows 306S and 306D,fall within the acceptable range, hence no imbalance correction weightamounts are indicated for the left and right correction planes. Further,as shown in FIG. 13, if the dimensions of the wheel are manually changedby the operator to indicate a 5.0 inch axial with and a 14.0 inchdiameter, (corresponding to the change shown in FIG. 6) withoutre-measuring the imbalance, the measured imbalance in the wheel remainsunchanged, as shown on the sliding scales 302 and 304. As a result, noimbalance correction weight amounts are indicated for the left and rightcorrection planes.

[0077] The method of the present invention provides a similar advantagewhen balancing large wheels. For example, as shown in FIG. 14, a wheelhaving a 8.0 inch axial width, and a 16.0 inch diameter might have animbalance above the threshold, as shown on sliding scales 302 and 304,resulting in the balancer displaying to an operator imbalance correctionweights required for both the left and right imbalance correctionplanes. However, as shown in FIG. 15, if the dimensions of the wheel aremanually changed by the operator to show an 18.0 inch diameter, withoutre-measuring the imbalance, less weight is required to correct the sameimbalance. As a result, the balancer indicates to an operator thatreduced weights in the left and right imbalance correction planes arestill required to correct the imbalance which is above the imbalancethreshold.

[0078] It is known that a rotating body 22 static imbalance force is afunction of the imbalance mass, the radial distance of the imbalancemass from the axis of rotation, and the angular velocity of the rotatingbody 22. In a vehicle wheel application, where the rotating body 22consists of a wheel rim and tire assembly, for any given vehicle speed,the angular velocity may be expressed as a function of the tire diameteror as a function of the tire diameter and the wheel rim diameter. Hence,in an alternate embodiment of the present invention, the imbalance forceF, experienced by a vehicle from a rotating wheel assembly may bedefined as: $\begin{matrix}{F = \frac{\left( \frac{v}{\pi \quad D_{T}} \right)^{2}m\quad D_{W}}{2}} & {{Equation}\quad (3)}\end{matrix}$

[0079] where v is the vehicle velocity, D_(T) is the tire diameter,D_(W) is the correction weight application diameter, which is equal tothe wheel diameter for clip-on weights, and m is the imbalance mass. Forexample, if an acceptable imbalance correction threshold or “blind” fora wheel rim having a diameter D_(W0) of 15.0″ with a tire having adiameter D_(T0) of 28.0″ is 0.29 oz. (m₀), an equation for calculatingan equivalent “blind” (m₁) for an assembly with the dimensions D_(W1)and D_(T1) is: $\begin{matrix}{m_{1} = {\frac{m_{0}D_{W0}}{D_{W1}}\left( \frac{D_{T1}}{D_{T0}} \right)^{2}}} & {{Equation}\quad (4)}\end{matrix}$

[0080] Once an acceptable imbalance correction threshold or “blind” isestablished for a particular tire and rim combination, an equivalentimbalance correction threshold or “blind” may be automaticallycalculated using Equation (4) for a wide variety of wheel assemblies,providing an imbalance correction threshold curve, such as shown inFIGS. 10A for wheel rim dimensions and in FIG. 10B for tire dimensions.

[0081] Utilizing the tire diameter D_(T), and the wheel diameter D_(W),wheel assemblies may be classified into predefined groupings. Forexample, performance wheel assemblies where D_(T)−D_(W) is relativelysmall (˜3.0 inches or less), touring wheel assemblies, where D_(T)−D_(W)is between 3.0″ and 5.0″, and truck wheel assemblies, where D_(T)−D_(W)is greater than 5.0″. Each different predefined grouping may be providedwith a different acceptable imbalance correction threshold or “blind”curve. Using Equation (4), the specific imbalance correction thresholdor “blind” for a wheel assembly having specific dimensions may beautomatically calculated, once a specific tire grouping and associatedcurve has been selected.

[0082] A similar analysis for the rotating body 22 couple imbalanceforce can be made. Where L is the wheel width, the imbalance couple (M)felt by the vehicle can be expressed as: $\begin{matrix}{M = {\left( \frac{v}{\pi \quad D_{T}} \right)^{2}w\quad L\frac{D_{W}}{2}}} & {{Equation}\quad 5}\end{matrix}$

[0083] If an acceptable imbalance correction threshold or “blind” for awheel assembly having a 15×6 inch wheel rim (D_(W0)×L₀), with a 28.0inch diameter tire (D_(T0)) installed thereon is 0.29 oz (w₀) then usingEquation 5, and equivalent blind (w₁) for an assembly with the dimensionD_(W1), D_(T1), and L₁ is: $\begin{matrix}{w_{1} = {\frac{w_{0}D_{w0}}{D_{w1}}\left( \frac{D_{T1}}{D_{T0}} \right)^{2}\frac{L_{0}}{L_{1}}}} & {{Equation}\quad 6}\end{matrix}$

[0084] Once an acceptable couple imbalance correction threshold or“blind” is established for a particular tire and rim combination, anequivalent couple imbalance correction threshold or “blind” may beautomatically calculated using Equation (6) for a wide variety of wheelassemblies, providing an couple imbalance correction threshold curve,such as shown in FIG. 11A for wheel rim dimensions and FIG. 11B for tiredimensions.

[0085] The present invention can be embodied in-part in the form ofcomputer-implemented processes and apparatuses for practicing thoseprocesses. The present invention can also be embodied in-part in theform of computer program code containing instructions embodied intangible media, such as floppy diskettes, CD-ROMs, hard drives, or another computer readable storage medium, wherein, when the computerprogram code is loaded into, and executed by, an electronic device suchas a computer, micro-processor or logic circuit, the device becomes anapparatus for practicing the invention.

[0086] The present invention can also be embodied in-part in the form ofcomputer program code, for example, whether stored in a storage medium,loaded into and/or executed by a computer, or transmitted over sometransmission medium, such as over electrical wiring or cabling, throughfiber optics, or via electromagnetic radiation, wherein, when thecomputer program code is loaded into and executed by a computer, thecomputer becomes an apparatus for practicing the invention. Whenimplemented in a general-purpose microprocessor, the computer programcode segments configure the microprocessor to create specific logiccircuits.

[0087] In view of the above, it will be seen that the several objects ofthe invention are achieved and other advantageous results are obtained.As various changes could be made in the above constructions withoutdeparting from the scope of the invention, it is intended that allmatter contained in the above description or shown in the accompanyingdrawings shall be interpreted as illustrative and not in a limitingsense.

1. A method of centering a rotating body on a balancer, comprising:mounting the rotating body on a spindle of the balancer; obtaining afirst measurement of at least one imbalance parameter of the rotatingbody on said spindle; altering the mounting of the rotating body on saidspindle; obtaining a current measurement of said at least one imbalanceparameter of the rotating body on said spindle; calculating a differencebetween said first measurement and said current measurement for said atleast one imbalance parameter; comparing said calculated difference withat least one predetermined threshold amount to determine whether therotating body is properly centered.
 2. The method of centering arotating body on a balancer as set forth in claim 1, wherein said stepof altering the mounting of the rotating body further comprises thesteps of loosening said mounting of the rotating body on said spindle,and tightening said mounting of the rotating body on said spindle. 3.The method of centering a rotating body on a balancer as set forth inclaim 2, wherein said loosening step comprises loosening a wing nut; andsaid tightening step comprises tightening said wing nut.
 4. The methodof centering a rotating body on a balancer as set forth in claim 2,wherein said step of altering the mounting of the rotating body furthercomprises the step of rotating the rotating body with respect to saidspindle after loosening said mounting and before tightening saidmounting.
 5. The method of centering a rotating body on a balancer asset forth in claim 1 further including the step of repeating, until atleast one calculated difference does not exceed said threshold amount,the steps of (a) altering the mounting; (b) obtaining a currentmeasurement; and (c) the additional step of calculating a differencebetween said current measurement and each previous measurement for saidat least one imbalance parameter.
 6. The method of centering a rotatingbody on a balancer as set forth in claim 1 wherein said rotating body isa wheel assembly consisting of a wheel rim and a tire.
 7. The method ofcentering a rotating body on a balancer as set forth in claim 1 whereinsaid rotating body is a wheel rim.
 8. The method of centering a rotatingbody on a balancer as set forth in claim 1 further including the step ofproviding an indication if said calculated difference exceeds saidthreshold amount.
 9. The method of centering a rotating body on abalancer as set forth in claim 1 wherein said at least one imbalanceparameter is an imbalance magnitude.
 10. The method of centering arotating body on a balancer as set forth in claim 9 where said imbalancemagnitude is an absolute imbalance magnitude selected from the setconsisting of static imbalance magnitude and dynamic imbalancemagnitude.
 11. The method of centering a rotating body on a balance asset forth in claim 9 where said imbalance magnitude is a computedimbalance correction weight amount.
 12. The method of centering arotating body on a balancer as set forth in claim 1 wherein said atleast one imbalance parameter is an imbalance angular location.
 13. Themethod of centering a rotating body on a balancer as set forth in claim1 wherein said at least one imbalance parameter is a transducer outputsignal.
 14. The method of claim 1 for centering a rotating body on abalancer wherein the balancer is a wheel balancer.
 15. The method ofclaim 1 for centering a rotating body on a balancer wherein the rotatingbody is a vehicle wheel assembly.
 16. A method of centering a wheelassembly on a wheel balancer, the wheel assembly including a wheel rimand a tire mounted on the wheel rim, comprising: mounting the wheelassembly on a spindle of the wheel balancer; obtaining a firstmeasurement of runout of the rim-mounted tire on said spindle; alteringthe mounting of the wheel assembly on said spindle; obtaining a currentmeasurement of said runout of the rim-mounted tire on said spindle;calculating a difference between said first measurement and said currentmeasurement for said runout; comparing said calculated difference with athreshold amount to determine whether the wheel assembly is properlycentered.
 17. The method of centering a wheel assembly on a wheelbalancer as set forth in claim 16 further including the step ofrepeating, until at least one calculated difference does not exceed saidthreshold amount, the steps of (a) altering the mounting; (b) obtaininga current measurement; and the additional step of calculating adifference between said current measurement and each previousmeasurement for said runout.
 18. The method of centering a wheelassembly on a wheel balancer as set forth in claim 16 further includingthe step of providing an indication if said calculated differenceexceeds said threshold amount.
 19. The method of centering a wheelassembly on a wheel balancer as set forth in claim 16 wherein saidrunout is a radial runout of an outer diameter of said rim-mounted tire.20. The method of centering a wheel assembly on a wheel balancer as setforth in claim 16 wherein said runout is a lateral runout of saidrim-mounted tire.
 21. A method for displaying, on a balancer, animbalance of a rotating body, comprising the steps of: establishing animbalance threshold; calculating an imbalance of the rotating body; andproviding a display of said calculated imbalance in relation to saidestablished imbalance threshold to an operator.
 22. The method of claim21 for displaying an imbalance of a rotating body wherein said imbalancethreshold is related to one or more dimensional characteristics of therotating body.
 23. The method of claim 21 for displaying an imbalance ofa rotating body wherein said provided display is a non-numeric display.24. The method of claim 21 for displaying an imbalance of a rotatingbody wherein the step of providing further includes generating fordisplay a scaled representation of both said calculated imbalance andsaid established imbalance threshold.
 25. The method of claim 21 fordisplaying an imbalance of a rotating body wherein the step ofcalculating an imbalance includes calculating an imbalance remaining inthe rotating body following application of one or more known imbalancecorrection weights at known positions.
 26. The method of claim 25 fordisplaying an imbalance of a rotating body wherein said imbalance is astatic imbalance.
 27. The method of claim 25 for displaying an imbalanceof a rotating body wherein said imbalance is a dynamic imbalance.
 28. Amethod for establishing an imbalance correction weight threshold levelin a balancer system configured to measure one or more imbalanceparameters of a rotating body, comprising the steps of: identifying atleast one dimension of the rotating body; selecting an imbalance limitassociated with each of said one or more imbalance parameters;calculating an imbalance correction weight threshold level for each ofsaid one or more imbalance parameters utilizing said identified at leastone dimension and said selected associated imbalance limit.
 29. Themethod of claim 28 wherein the step of identifying at least onedimension includes identifying a diameter of the rotating body; andwherein the step of calculating includes utilizing said identifieddiameter and a selected imbalance limit associated with a staticimbalance of said rotating body.
 30. The method of claim 29 wherein thestep of calculating includes solving the equation$W_{BS} = \frac{F_{MAX}}{\left( \frac{D}{2} \right)}$

where W_(BS) is the imbalance correction weight threshold level, F_(MAX)is the selected imbalance limit associated with a static imbalance ofthe rotating body, and D is the diameter of the correction weight circleof the rotating body.
 31. The method of claim 28 wherein the step ofidentifying at least one dimension includes identifying a diameter andan axial width for placing correction weights on the rotating body; andwherein the step of calculating includes utilizing said identifieddiameter, said identified axial width, and a selected imbalance limitassociated with a dynamic imbalance of said rotating body.
 32. Themethod of claim 31 wherein the step of calculating includes solving theequation W _(BD) =M _(MAX)/(W×D/2) where W_(BD) is the correction weightthreshold level for dynamic imbalance M_(max) is the selected imbalancelimit associated with a dynamic imbalance of the rotating body, W is theaxial distance between the weight placement planes of the rotating body,and D is the diameter of the weight placement planes of the rotatingbody.
 33. A method for establishing imbalance correction weightthreshold levels in a balancer system configured to measure a staticimbalance parameter and a dynamic imbalance parameter of a rotatingbody, comprising the steps of: identifying a diameter of the rotatingbody; identifying an axial width of the rotating body; selecting animbalance limit associated with said static imbalance parameter;selecting an imbalance limit associated with said dynamic imbalanceparameter; calculating an imbalance correction weight threshold levelfor said static imbalance parameter utilizing said identified diameterand said selected imbalance limit associated with said static imbalanceparameter; calculating an imbalance correction weight threshold levelfor said dynamic imbalance parameter utilizing said identified diameter,said identified axial width, and a selected imbalance limit associatedwith said dynamic imbalance parameter.
 34. A method for balancing avehicle wheel utilizing the calculated imbalance correction weightthreshold levels for static imbalance parameters and dynamic imbalanceparameters as set forth in claim 33, comprising the steps of: obtaininga measurement of static and dynamic imbalance in the vehicle wheel;determining static and dynamic imbalance correction weights for thevehicle wheel based upon said obtained measurements of static anddynamic imbalance; selecting, responsive to said determined staticimbalance correction weight exceeding said calculated imbalancecorrection weight threshold level for said static imbalance and to saiddetermined dynamic imbalance correction weight being less than saidcalculated imbalance correction weight threshold level for said dynamicimbalance, a placement position for said static imbalance correctionweight which reduces said measurement of dynamic imbalance in thevehicle wheel.
 35. The method of claim 34 for balancing a vehicle wheelwherein the step of selecting a placement position for said staticimbalance correction weight includes: calculating a static imbalancecorrection weight placement phase angle; calculating an inner wheelplane dynamic imbalance correction weight placement phase angle;calculating an outer wheel plane dynamic imbalance correction weightplacement phase angle; identifying one of said inner and outer wheelplane dynamic imbalance correction weight placement phase angles whichis nearest to said static imbalance correction weight placement phaseangle; and placing said static imbalance correction weight at saidcalculated static imbalance correction weight placement phase angle in awheel plane corresponding to the wheel plane of said nearest identifieddynamic imbalance correction weight placement phase angle.
 36. A methodfor establishing a static imbalance correction weight threshold levelfor a grouping of vehicle wheel assemblies having similarcharacteristics in a vehicle wheel balancer system configured to measureone or more imbalance parameters of a vehicle wheel assembly, comprisingthe steps of: establishing an acceptable static imbalance correctionweight threshold for a vehicle wheel assembly in the grouping of vehiclewheel assemblies, said vehicle wheel assembly having a known wheel rimdiameter and a known tire diameter; identifying a vehicle wheel rimdiameter and a tire diameter for a vehicle wheel assembly in thegrouping of vehicle wheel assemblies having an unknown imbalance;calculating a static imbalance correction weight threshold level saidvehicle wheel assembly having an unknown imbalance utilizing theequation${m_{1} = {\frac{m_{0}D_{W0}}{D_{W1}}\left( \frac{D_{T1}}{D_{T0}} \right)^{2}}}\quad$

where m₁ is the calculated static imbalance correction weight thresholdlevel; m₀ is the established acceptable static imbalance correctionweight threshold level; D_(W0) is the known wheel rim diameter; D_(T0)is the known tire diameter; D_(W1) is the identified wheel rim diameterfor said vehicle wheel assembly having an unknown imbalance; and D_(T1)is the identified tire diameter for said vehicle wheel assembly havingan unknown imbalance.
 37. A method for selecting an imbalance correctionweight threshold level for a vehicle wheel assembly having an unknownimbalance in a vehicle wheel balancer system configured to measure oneor more imbalance parameters of a vehicle wheel assembly, comprising thesteps of: identifying a grouping of vehicle wheel assemblies havingsimilar characteristics to the vehicle wheel assembly having the unknownimbalance; identifying an associated acceptable imbalance correctionweight threshold curve for said identified grouping of vehicle wheelassemblies; and determining a specific imbalance correction weightthreshold for the vehicle wheel assembly having the unknown imbalancefrom said identified acceptable imbalance correction weight thresholdcurve and one or more characteristics of the vehicle wheel assemblyhaving the unknown imbalance.
 38. The method for selecting an imbalancecorrection weight threshold level of claim 37 wherein said specificimbalance correction weight threshold is a static imbalance correctionweight threshold.
 39. The method for selecting an imbalance correctionweight threshold level of claim 37 wherein said specific imbalancecorrection weight threshold is a couple imbalance correction weightthreshold.
 40. A method for establishing a couple imbalance correctionweight threshold level for a grouping of vehicle wheel assemblies havingsimilar characteristics in a vehicle wheel balancer system configured tomeasure one or more imbalance parameters of a vehicle wheel assembly,comprising the steps of: establishing an acceptable couple imbalancecorrection weight threshold for a vehicle wheel assembly in the groupingof vehicle wheel assemblies, said vehicle wheel assembly having a knownwheel rim diameter, wheel rim width, and a known tire diameter;identifying a vehicle wheel rim diameter, a wheel rim width, and a tirediameter for a vehicle wheel assembly in the grouping of vehicle wheelassemblies having an unknown imbalance; calculating a couple imbalancecorrection weight threshold level said vehicle wheel assembly having anunknown imbalance utilizing the equation$w_{1} = {\frac{w_{0}D_{w0}}{D_{w1}}\left( \frac{D_{T1}}{D_{T0}} \right)^{2}\frac{L_{0}}{L_{1}}}$

where w₁ is the calculated couple imbalance correction weight thresholdlevel; w₀ is the established acceptable couple imbalance correctionweight threshold level; D_(W0) is the known wheel rim diameter; D_(T0)is the known tire diameter; D_(W1) is the identified wheel rim diameterfor said vehicle wheel assembly having an unknown imbalance; D_(T1) isthe identified tire diameter for said vehicle wheel assembly having anunknown imbalance; L₀ is the known wheel rim width; and L₁ is theidentified wheel rim width for said vehicle wheel assembly having anunknown imbalance.